QICS: Quantum Information Conic Solver

Abstract: We introduce QICS (Quantum Information Conic Solver), an open-source primal-dual interior point solver fully implemented in Python, which is focused on solving optimization problems arising in quantum information theory. QICS has the ability to solve optimization problems involving the quantum relative entropy, noncommutative perspectives of operator convex functions, and related functions. It also includes an efficient semidefinite programming solver which exploits sparsity, as well as support for Hermitian matrices. QICS is also currently supported by the Python optimization modelling software PICOS. This paper aims to document the implementation details of the algorithm and cone oracles used in QICS, and serve as a reference guide for the software. Additionally, we showcase extensive numerical experiments which demonstrate that QICS outperforms state-of-the-art quantum relative entropy programming solvers, and has comparable performance to state-of-the-art semidefinite programming solvers.